We consider dependent site percolation on the two-dimensional square lattice, the underlying probability measure being invariant and ergodic under each of the translations and invariant under axis reflections. If this measure satisfies the FKG condition and if percolation occurs, then we show that the infinite occupied cluster is unique with probability 1, and that all vacant star-clusters are finite

On the uniqueness of the infinite occupied cluster in dependent two-dimensional site percolation / A. Gandolfi;M. Keane;L. Russo. - In: ANNALS OF PROBABILITY. - ISSN 0091-1798. - STAMPA. - 16:(1988), pp. 1147-1157. [10.1214/aop/1176991681]

On the uniqueness of the infinite occupied cluster in dependent two-dimensional site percolation

GANDOLFI, ALBERTO;
1988

Abstract

We consider dependent site percolation on the two-dimensional square lattice, the underlying probability measure being invariant and ergodic under each of the translations and invariant under axis reflections. If this measure satisfies the FKG condition and if percolation occurs, then we show that the infinite occupied cluster is unique with probability 1, and that all vacant star-clusters are finite
1988
16
1147
1157
A. Gandolfi;M. Keane;L. Russo
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/655674
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